Comprehensive evaluation of Luzhou‐flavor liquor quality based on fuzzy mathematics and principal component analysis

Abstract Currently, the primary method of identifying high‐ and low‐quality liquors is sensory tasting, which is prone to uncertainty caused by the biases of tasters. To address this problem, this study used color, aroma, taste, and style as four factors affecting the sensory quality of Luzhou‐flavor liquor; determined the weights of each factor; and quantitatively evaluated the sensory quality of five different Luzhou flavor liquor using fuzzy mathematical methods. The volatile aromatic substances in the liquor samples were detected by GC‐MS, and analyzed using principal component analysis. The results obtained from fuzzy mathematics and principal component analysis indicated that the comprehensive evaluation system was scientifically sound and reasonably constructed.


| INTRODUC TI ON
Chinese liquors are the traditional fermented distilled liquors of China (Zheng & Han, 2016). Luzhou-flavor liquors, one of the twelve major aromatic liquors in China, have unique flavors and aromas, and account for more than 70% of annual liquor yields in China (He et al., 2019). Luzhou-flavor liquors are produced from grains with medium-high temperature, with Daqu being the aroma-producing agent, and involve continuous distillation of grain ingredients, mixed steaming and mixed burning, solid-state fermentation, distillation, aging, and blending. Their aromatic compounds are dominated by ethyl caproate, and are produced without the addition of edible alcohols, nonfermented aromatic compounds, or taste-producing substances Shi et al., 2011).
Fuzzy mathematics is a mathematical theory and method for studying and processing fuzzy phenomena . It can quantify unclear or unquantifiable boundaries, and scientifically and comprehensively evaluate the multiple quality indicators of the target (Dong & Bi, 2020;Minaev et al., 2020). Sensory evaluation is currently the primary method for determining liquor quality, blending, and flavoring. Traditional sensory evaluation methods generally adopt weighted averaging and total scoring, which are affected by factors like the region, ethnicity, habits, liquor tasting environment, hobbies, and psychological factors of individuals (Cheng et al., 2013;Mukhopadhyay et al., 2013), creating a certain fuzziness. Hence, fuzzy mathematics is suitable for the mathematical and quantitative description/processing of the results of sensory evaluation . It can eliminate the subjectivity and unilateralism of sensory evaluation (Morales & Boekel, 1997), and thus provide more accurate, objective, reasonable, and scientific evaluation results (Xu et al., 2019;Zou et al., 2019). To date, fuzzy mathematics and sensory evaluation have been combined in research on pit mud (Chang et al., 2018), jams (Shinde & Kulkarni, 2016), yellow rice liquors (Feng et al., 2018), tea (Debjani et al., 2013), sauce (Zhou & Wei, 2019), sausage (Lee & Kwon, 2007), agricultural products and insecticides (Cheng et al., 2021), Radix pseudostellariae healthcare liquors , and wine (Song et al., 2021).
Principal component analysis (PCA) is a statistical method that converts multiple variables into a few principal components through dimensionality reduction. This method can, therefore, solve problems involving multiple inter-related variables (Abdi & Williams, 2010). PCA combines several detection techniques, and is used for the analysis of foods and drugs (Pravdova et al., 2002;Wang et al., 2020). Trace components in liquors are mainly analyzed using gas chromatography-mass spectrometry (GC-MS; Fan et al., 2019).
Research on trace components can reveal the fermentation mechanism of liquors, and is, therefore, vital for understanding their aroma characteristics and overall quality Yan et al., 2020).
The results of chromatography are processed by PCA to develop a more objective and effective method for liquor quality evaluation.
However, till date there is no report of fuzzy mathematics being used for the evaluation of Luzhou-flavor liquors, nor are there reports of using PCA for the comprehensive analysis of the physiochemical indicators of liquors. Therefore, this study aimed to determine the weights of liquor sensory indicators (color, aroma, taste, and style) and use fuzzy mathematics to quantitatively evaluate the sensory quality of five different Luzhou-flavor liquor samples. Subsequently, PCA was used for dimensionality reduction of trace components in liquors, statistical analysis, and for the establishment of a comprehensive and scientific mathematical model. The findings of this study will help in the construction of a comprehensive evaluation system for Luzhou-flavor liquors.

| Materials and reagents
Luzhou-flavor liquors with five quality levels (newly produced liquor blended in different proportions with old liquor by the liquor company; the higher the percentage of newly produced liquor, the lower is its quality) were bought from a liquor factory in Henan.

| Sensory evaluation
Four evaluation grades of Luzhou-flavor liquors (Table 1)  Methods for Liquors). To ensure the accuracy of evaluation and the environmental comfort, we asked the liquor tasters to refrain from drinking, smoking, and eating spicy or irritating foods 24 h before evaluation.
They waited for 10 min between evaluations and gargled with clean water during these intervals. Ten tasters (five males and five females) with certificates of liquor evaluation and majoring in liquor-making engineering, were invited to constitute the evaluation team. Liquor tasters have a background in the systematic theoretical study and practice of brewing and tasting. They are, therefore, trained to earnestly comprehend and understand the relevant evaluation indices, and be objective and fair in their assessment. Based on the grade standards, a singlefactor evaluation involving four indicators (color, aroma, taste, and style) was conducted, and an evaluation table was filled in. With a maximum score of 100, scores of >95, 90-95, 85-90, and 80-85, were considered excellent grade, grade 1, grade 2, and grade 3, respectively.

| Determination of fuzzy matrix
The 10 evaluators scored the liquor samples according to the comment set V. The times of comments given to each index were then plotted in a table. The data in the table were divided by 10 to determine the membership grade R of each of the four factors, for the five liquor samples. A membership grade matrix was obtained by arranging the factors in rows. According to the principle of fuzzy transformation, Y was used as a synthetic evaluation set that contains the products to be evaluated. Therefore, a fuzzy relationship evaluation set was obtained: Y = XR, where X is a weight set and R is a fuzzy matrix. Finally, a comprehensive score matrix T is introduced to process the fuzzy relationship evaluation set Y. According to the specialties of sensory evaluation, let the evaluation grade set be K = {k 1 , k 2 , k 3 , k 4 }. The total score in the fuzzy comprehensive evaluation of liquor samples was T = Y × K, where the evaluation grade set was K = {90, 70, 50, 30}.

| Chromatographic conditions
The chromatographic column used was SHIMADZU Rxi-5MS capillary column (30 × 0.25 mm, 0.25 μm) with an inlet temperature of 250 ℃ and a column flow of 1.0 ml/min. The sampling method involved splitless injection and heating according to the following program: the starting temperature was 40°C (held for 2 min), was increased at 3.5°C/min to 95°C (held for 2 min), and then increased at 5°C/min to 230°C (held for 10 min); an injection volume of 1 μl was used.

| Mass spectrometry conditions
Ion source was from EI and the scan mode used was SCAN mode, the ion source temperature was 220°C, interface temperature was 250°C, electronic capacity was 70 eV, detector voltage was 0.7 kV, solvent delay was by 3.0 min, and scanning range was 30-550 amu.

| Data processing
The data obtained were used for statistical analysis and PCA using all-cause models in Microsoft Office Excel 2016 and SPSS 26.0. The significance level was set at p < .05. the grading criteria developed for dark wine evaluation and singlefactor evaluation ( Table 1). The five wine samples were poured into numbered wine glasses by a special person, and evaluated and scored by the ten tasters. The evaluation results were collected, summarized, and statistically analyzed, to produce a statistical table of comprehensive tasting results (counting the number of sensory tasters) ( Table 2).

| Trace component analysis of liquor samples
The aromatic components of the five liquor samples were detected using GC-MS. Then, GC-MS total ion current maps of the representative components in the liquor samples were plotted. The chromatogram components of the Luzhou-flavor liquors are listed in Table 3.
The chromatogram results of the Luzhou-flavor liquors were not quantitatively analyzed, and were all relative concentrations (%).

| PCA mathematical model
The PCA mathematical model is as follows: where a 1i , a 2i , a ni (i = 1, n) are the eigenvectors of the eigenvalues in the covariance matrix Σ from V, and ZV 1 , ZV 2 , ……, ZV m are the standard-

TA B L E 8 Correlation between
Luzhouflavor liquor model scores and sensory scores the loss of information is small, indicating that several common factors extracted in this study can strongly explain these variables.
The eigenvalues and variance contribution rates of the principal components obtained from the Luzhou-flavor liquors by PCA are listed in Table 5. Principal components with eigenroots larger than 1 and accumulative contribution rates larger than 80% were selected as the study targets. As shown in Table 5, the eigenroots of the first, second, and third principal components are 6.184, 4.337, and 1.163, respectively (all larger than 1), and their accumulative contribution rates are 51.536%, 87.680%, and 97.371%, respectively, which can efficiently reflect the original data in the indices of the Luzhou-flavor liquors.
The eigenvectors were calculated based on the eigenroots of the first three principal components and the load matrix ( Table 6).
The standardized V 1 , V 2 , V 3 V 12 values are marked as ZV 1 to ZV 12 , respectively. Thus, the principal components are expressed as: where the coefficients are the eigenvectors of the quality indices, and F 1 , F 2 , and F 3 are the scores of the principal components. The variance contribution rates βi (i = 1, 2, 3) of the initial eigenroots were used as the weighting coefficients of the first three principal components.
Thereby, a quality evaluation model of the Luzhou-flavor liquors, namely, the comprehensive score, was obtained in Equation (4): The principal component matrix can also be used to measure the contributions of the principal components. Specifically, a larger absolute value of the load means that the contribution of the corresponding principal component is larger (Karytsas & Choropanitis, 2017). The first principal component has large loads in V 1 , V 4 , V 10 , V 11 , and V 12 , and mainly influences the liquor quality from the perspectives of ethyl caproate, ethyl butyrate, furfural, heptanoic acid, and octanoic acid ( Table 6). The second principal component has large loads in V 6 , V 7 , V 8 , and V 9 , and mainly influences the liquor quality from the perspectives of 2-methyl-1-propanol, butanol, isopentyl alcohol, and hexyl alcohol.
The third principal component has large loads in V 2 , V 3 , and V 5 , and mainly influences the liquor quality from the perspectives of ethyl octanoate, ethyl lactate, and butyl caproate.

| Trace components by PCA
The comprehensive quality scores of Luzhou-flavor liquors were determined using Equation (4) ( Table 7). From the PCA-based mathematical model, the scores of the five samples of Luzhou-flavor liquors were ranked from high to low as M3, M1, M4, M2, and M5.

| Correlations of the Luzhou-flavor liquor model
Correlations and significance between the model-based comprehensive scores, F, and the sensory scores, were tested ( Table 8) (C3060020). We thank Wiley editing services for English language editing.

CO N FLI C T O F I NTE R E S T
The authors declare no conflict of interest.

E TH I C S S TATEM ENT
Our research did not contain any animal experiments or human subjects.

DATA AVA I L A B I L I T Y S TAT E M E N T
Data available on request from the authors.